Whakaoti i te -3x^2+5.1x-1.56=0

$$- 3 x ^ { 2 } + 5.1 x - 1.56 = 0$$

Whakaoti mō x

$$x=1.3$$

$$x=0.4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-3x^{2}+5.1x-1.56=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, 5.1 mō b, me -1.56 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5.1±\sqrt{5.1^{2}-4\left(-3\right)\left(-1.56\right)}}{2\left(-3\right)}$$

Pūruatia 5.1 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-5.1±\sqrt{26.01-4\left(-3\right)\left(-1.56\right)}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-5.1±\sqrt{26.01+12\left(-1.56\right)}}{2\left(-3\right)}$$

Whakareatia 12 ki te -1.56.

$$x=\frac{-5.1±\sqrt{26.01-18.72}}{2\left(-3\right)}$$

Tāpiri 26.01 ki te -18.72 mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{-5.1±\sqrt{7.29}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 7.29.

$$x=\frac{-5.1±\frac{27}{10}}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{-5.1±\frac{27}{10}}{-6}$$

Nā, me whakaoti te whārite x=\frac{-5.1±\frac{27}{10}}{-6} ina he tāpiri te ±. Tāpiri -5.1 ki te \frac{27}{10} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=-\frac{\frac{12}{5}}{-6}$$

Whakawehe -\frac{12}{5} ki te -6.

$$x=\frac{2}{5}$$

Nā, me whakaoti te whārite x=\frac{-5.1±\frac{27}{10}}{-6} ina he tango te ±. Tango \frac{27}{10} mai i -5.1 mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=-\frac{\frac{39}{5}}{-6}$$

Whakawehe -\frac{39}{5} ki te -6.

$$x=\frac{13}{10}$$

Kua oti te whārite te whakatau.

$$x=\frac{2}{5} x=\frac{13}{10}$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-3x^{2}+5.1x-1.56=0$$

Me tāpiri 1.56 ki ngā taha e rua o te whārite.

$$-3x^{2}+5.1x-1.56-\left(-1.56\right)=-\left(-1.56\right)$$

Mā te tango i te -1.56 i a ia ake anō ka toe ko te 0.

$$-3x^{2}+5.1x=-\left(-1.56\right)$$

Tango -1.56 mai i 0.

$$-3x^{2}+5.1x=1.56$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3x^{2}+5.1x}{-3}=\frac{1.56}{-3}$$

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

$$x^{2}+\frac{5.1}{-3}x=\frac{1.56}{-3}$$

Whakawehe 5.1 ki te -3.

$$x^{2}-1.7x=\frac{1.56}{-3}$$

Whakawehe 1.56 ki te -3.

$$x^{2}-1.7x=-0.52$$

Whakawehea te -1.7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -0.85. Nā, tāpiria te pūrua o te -0.85 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-1.7x+\left(-0.85\right)^{2}=-0.52+\left(-0.85\right)^{2}$$

Pūruatia -0.85 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-1.7x+0.7225=-0.52+0.7225$$

Tāpiri -0.52 ki te 0.7225 mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-1.7x+0.7225=0.2025$$

Tauwehea x^{2}-1.7x+0.7225. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-0.85\right)^{2}=0.2025$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x-0.85\right)^{2}}=\sqrt{0.2025}$$

Whakarūnātia.

$$x-0.85=\frac{9}{20} x-0.85=-\frac{9}{20}$$

Me tāpiri 0.85 ki ngā taha e rua o te whārite.

$$x=\frac{13}{10} x=\frac{2}{5}$$